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When x/y = 1.2, (x^2-y^2)/(x^2+y^2) =?

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When x/y = 1.2, (x^2-y^2)/(x^2+y^2) =? [#permalink]

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[GMAT math practice question]

When x/y = 1.2, (x^2-y^2)/(x^2+y^2) =?

A. 10/51
B. 11/51
C. 10/61
D. 11/61
E. 11/71
[Reveal] Spoiler: OA

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Last edited by Bunuel on 01 Nov 2017, 05:16, edited 1 time in total.
Edited the OA.

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Re: When x/y = 1.2, (x^2-y^2)/(x^2+y^2) =? [#permalink]

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New post 01 Nov 2017, 02:22
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MathRevolution wrote:
[GMAT math practice question]

When x/y = 1.2, (x^2-y^2)/(x^2+y^2) =?

A. 10/51
B. 11/51
C. 10/61
D. 11/61
E. 11/71


\(\frac{x}{y}=1.2\), square both sides to get \(\frac{x^2}{y^2}=1.44\) -------(1)

subtract \(1\) from both sides of equation (1)

\(\frac{x^2}{y^2}-1=1.44-1\)

or \(\frac{{x^2-y^2}}{y^2}=0.44\)

Now add \(1\) to both sides of equation (1)

\(\frac{x^2}{y^2} + 1=1.44+1\)

or \(\frac{{x^2+y^2}}{y^2}=2.44\)

so \(\frac{x^2-y^2}{x^2+y^2} = \frac{0.44}{2.44} = \frac{11}{61}\)

Option D

Hi Bunuel

Can you confirm the answer or point out errors in my approach because OA is E i.e 11/71

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Re: When x/y = 1.2, (x^2-y^2)/(x^2+y^2) =? [#permalink]

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New post 01 Nov 2017, 05:16
niks18 wrote:
MathRevolution wrote:
[GMAT math practice question]

When x/y = 1.2, (x^2-y^2)/(x^2+y^2) =?

A. 10/51
B. 11/51
C. 10/61
D. 11/61
E. 11/71


\(\frac{x}{y}=1.2\), square both sides to get \(\frac{x^2}{y^2}=1.44\) -------(1)

subtract \(1\) from both sides of equation (1)

\(\frac{x^2}{y^2}-1=1.44-1\)

or \(\frac{{x^2-y^2}}{y^2}=0.44\)

Now add \(1\) to both sides of equation (1)

\(\frac{x^2}{y^2} + 1=1.44+1\)

or \(\frac{{x^2+y^2}}{y^2}=2.44\)

so \(\frac{x^2-y^2}{x^2+y^2} = \frac{0.44}{2.44} = \frac{11}{61}\)

Option D

Hi Bunuel

Can you confirm the answer or point out errors in my approach because OA is E i.e 11/71

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Edited the OA. It's D.
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Re: When x/y = 1.2, (x^2-y^2)/(x^2+y^2) =? [#permalink]

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New post 04 Nov 2017, 06:02
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When x/y = 1.2, (x^2-y^2)/(x^2+y^2) =?

A. 10/51
B. 11/51
C. 10/61
D. 11/61
E. 11/71

x/y=1.2(fraction wise which is 6/5)
therefore x=6 & y=5

(x^2-y^2)/(x^2+y^2)= (x+y)(x-Y)/(X^2+y^2)
which will be= (6+5)(6-5)/(6^2+5^2)= 11/61

:D

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When x/y = 1.2, (x^2-y^2)/(x^2+y^2) =? [#permalink]

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New post 04 Nov 2017, 18:20
=>

x/y = 6/5.
(x^2-y^2)/(x^2+y^2) = ((x/y)^2-1)/((x/y)^2+1) = ((6/5)^2 – 1 ) / ((6/5)^2 + 1 )
= (6^2-5^2)/(6^2+5^2) = (36-25)/(36+25) = 11/61

Therefore, the answer is D.
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When x/y = 1.2, (x^2-y^2)/(x^2+y^2) =?   [#permalink] 04 Nov 2017, 18:20
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